There are several ways to catch back up when playing Jax. He has incredible dueling power, a great surprise duel kit, unparalleled hybrid damage, and with Gunblade and some life steal items, he can nearly become a drain tank. Jax also can build almost any item and still benefit, thanks to his versatile kit. These factors add up to many ways to regain ground.
In general, all involve either trying to delay the game or increase your gold income until you reach full build, as Jax has one of the most dangerous late games of any champion, which people often forget (a full build Jax can solo Elder Drake, take lesser drakes and towers in seconds, and is practically invincible in a duel). This usually entails cooperating with your allies to gank a single bulky target, or attempting to instigate a duel with a squishy target on the enemy team.
If you're playing Jax as the Jungler, keep in mind that your E is a devastating tool against any ADC, and certain AD midlaners if you're playing top.
As an aside, Jax is very map rotation oriented.
It allows you to dodge autoattacks, dealing damage based on how many you absorbed, and also stun the enemy champ long enough to let your passive stack up (You can also auto attack while using this ability, even though Jax is busy spinning his lamp above his head). Make sure you have a warding trinket, and pay attention to it.
This ability also reduces AOE damage by 20%, and dodges minion autoattacks, so it can be effectively used against certain tanks and midlane champions with AOE.
Use this tool at the start of ganks on the bottom lane. Either the enemy ADC will run away, and leave you with their minions (thus giving you gold and pushing you closer to full build) or they will stay, and with the help of your bottom duo, an assist or kill is all but
teed (which, again, gives you the gold needed to bring you to your powerful end game).
However, say perhaps the enemy has already transitioned to the grouped phase. Remember your warding trinket? Many people forget that Jax's Q can also be used on allies, including wards. By keeping the Jungle well-warded, you not only get better vision and can single out squishy champions more, but you also gain mobility for escapes and ambushes.
Are you getting killed too much? Jax is also surprisingly durable if itemized correctly. Once you hit level six, Jax's ultimate will give you an incredibly high boost to resistances, and can temporarily turn our Grandmaster at arms into a super mobile Juggernaut capable of tangling with the best champions League has to offer. I recommend building damage items with some sort of lifesteal, and also a Spirit Visage if you happen to be fighting a team heavy on magic damage. Hextech Gunblade is almost a must: it provides hybrid damage, spell vamp and life steal, and a great active for initiating fights. Keep in mind, your ultimate's active is based off of AP and AD, not armor and MR, so Gunblade will also serve to make you nigh unkillable during your ultimate. Since Jax is tailored to fighting ADCs, too, Randuin's Omen is a great item, providing an attack speed slow, a slow for enemies, and critical strike reduction! These three items combined with your ultimate turn Jax into an incredibly dangerous bruiser. The downside is that these items cost a lot of gold, and you will have to make sure to farm a great deal to stay on pace to catch up, be it in the Jungle or Lane.
Are you getting blown up in every team fight? That makes sense. Jax is not a teamtighting champion. However, if the enemy is occupied by going everywhere together, you can take advantage of Jax's passive to it's full extent: Jax is a split pushing monster. No, he is not mobile in the map-wide sense unless the jungle is lit up like a Christmas tree (thank you ward jumps), but outside of the ADC class you'd be hard pressed to find champions who can take turrets faster.
Other general Jax-is-behind Tips:
You need to keep your passive stacked to deal your full damage potential, so attack speed is a must. It allows you to stack faster. Also, avoid enemy champions with lots of CC, as they can put an end to your stacks with one good stun or root.
Jax's Leap Strike can be used on allies as well as enemies, so it's a defensive tool as well. If the fight isn't going well, leap to a friendly champion, minion, or ward away from the fight, and run!
If you need a quick burst of damage and the fight is going poorly, your W- Empower will reset your autoattack, thus allowing you to quickly put in two autoattacks (and with enough cool down reduction and attack speed, you can get in almost three per second, thus allowing you to proc your ultimate's passive with incredible efficiency).